Problem solving with simultaneous equations

12 questions

1. Solve using any method: 5x + 4y = 11 and 2x + 5y = 35. Write your answer in the form (x,y).
2. Solve using any method: x + 5y =24 and 10x + 6y = 20. Write your answer in the form (x,y).
3. Solve using any method: 8x + 2y =10 and 6x - 8y = 36. Write your answer in the form (x,y).
4. Solve using any method: 12x + 4y = 60 and 12x - 10y =102. Write your answer in the form (x,y).
5. Solve using any method: 3x + y = 15 and 10x - 10y = 90. Write your answer in the form (x,y).
6. Solve using any method: 3x + 5y = -6 and 10x - 10y = 60. Write your answer in the form (x,y).
7. Which two equations represent this scenario: Nine small bags (s) and five bigger bags (b) contains 182 counters in total.Two small bags and four bigger bags contain 104 counters in total.
8. Which two equations represent this scenario: Five small bags (s) and three bigger bags (b) contains 94 counters in total. Seven small bags and four bigger bags contain 128 counters in total.
9. A bakery sells cookies in boxes of small and large sizes. Four small and three large boxes contain 235 cookies. Two small boxes and five large boxes contain 275 cookies. How many are in each box?
10. A farmer sells bags of apples and oranges. Three bags of apples and four bags of oranges weigh 73 kg. Five bags of apples and three bags of oranges weigh 85 kg. What is the weight of each bag?
11. A company produces two types of gadget: standard (s) and premium (p). Selling 5 s and 3 p gadgets makes £260. Selling 3 s and 5 p gadgets makes £220. How much does each type of gadget cost?
12. A company produces two types of gadget: standard (s) and premium (p). Selling 6 s and 4 p gadget makes £560. Selling 4 s and 6 p gadgets makes £640. How much does each type of gadget cost?

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